Police in the US state of Michigan are holding a 50-year-old Canadian man in connection with the stabbing of a police officer at a regional airport that is being investigated as terrorism.

The suspect shouted "Allahu akbar" - the Arabic phrase for "god is greatest" - and expressed hatred for the United States before the attack on Wednesday morning, according to investigators.

FBI agent David Gelios identified the suspect as Amor Ftouhi, saying he was taken into custody at the scene and charged with committing an act of violence at an international airport.

Later Wednesday, Canadian police descended on an apartment in eastern Montreal that is connected to the suspect.

The stabbing occurred at about 9:45 am (1345 GMT) at Bishop International Airport in Flint, Michigan - about 100 kilometres north-west of Detroit.

The officer, Lieutenant Jeff Neville, was stabbed in the neck. He underwent surgery and was in stable condition, according to authorities, speaking at a news conference.

Ftouhi arrived in the United States on Friday after crossing the border at the Lake Champlain border crossing in upstate New York, Gelios said. He made his way to Flint and walked around inside the airport, leaving some baggage in a restroom before the attack.

There was no interaction between the suspect and the officer before the stabbing, Gelios said, describing the knife used as 30 centimetres long with a serrated blade about 20 centimetres long.

"He said something to the effect of you have killed people in Syria, Iraq and Afghanistan. We are all going to die," Gelios said, adding "he has a hatred for the United States."

Gelios said Ftouhi was the only suspect. The bureau said earlier that agents believed the stabbing was an "isolated incident."

The airport was evacuated and closed after the attack. All passengers were safe, Flint authorities said.

A Facebook profile under the name Amor Ftouhi lists his birth place as Tunis, Tunisia. It says Ftouhi studied at the University of Tunis and at Sullivan College in Montreal. Nothing at the site is connected to jihadist propaganda.